Summary  
This chapter demonstrates how to implement code that uses random number generation, loops, and running accumulators to simulate repeated trials and compute sample means illustrating convergence.  

General domain of usage  
Monte Carlo simulation in statistical analysis.

import unittest
import importlib
import numpy as np
import re

def _dynamic_test(test_case, condition, success_message, failure_message):
    if condition:
        test_case._testMethodName = success_message
        test_case.assertTrue(True)
    else:
        test_case._testMethodName = failure_message
        test_case.fail(failure_message)


class TestUserCode(unittest.TestCase):

    def test_function_exists(self):
        import user_code
        _dynamic_test(
            self,
            hasattr(user_code, "simulate_law_of_large_numbers"),
            "The function `simulate_law_of_large_numbers` is declared.",
            "Expected the function `simulate_law_of_large_numbers` to be declared."
        )

    def test_random_generation_used(self):
        with open("user_code.py", "r") as f:
            code = f.read()

        pattern = r"np\.random\.randn"
        _dynamic_test(
            self,
            re.search(pattern, code) is not None,
            "Random sampling from a normal distribution is used.",
            "Expected sampling using `np.random.randn`."
        )

    def test_running_mean_computation_present(self):
        with open("user_code.py", "r") as f:
            code = f.read()

        pattern = r"np\.cumsum"
        _dynamic_test(
            self,
            re.search(pattern, code) is not None,
            "Running mean computation is present.",
            "Expected running mean using cumulative sum."
        )


if __name__ == "__main__":
    unittest.main()

test_main.py

Master the essentials of simulation and Monte Carlo modeling in Python. Learn to generate random samples, build uncertainty models, estimate risk, and simulate simple financial scenarios using practical code and hands-on exercises.

Explore the basics of random number generation, probability distributions, and reproducibility in Python. Build a strong foundation for simulation by understanding how randomness is modeled and controlled.

Apply Monte Carlo methods to model uncertainty, estimate risk, and analyze probabilistic outcomes. Learn to run multi-simulation loops and interpret results.

Apply simulation techniques to simple financial models, including portfolio returns, random walks, and toy pricing scenarios. Aggregate outcomes and estimate practical risk.

Law of Large Numbers via Simulation

Solution

Law of Large Numbers via Simulation

Solution